Some issues in a gauge model of unparticles

Abstract

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and the Ward identity of the physical amplitudes. We find that non-integrable singularities arise in physical quantities like the cross section and the decay rate from the gauge interactions of unparticles. We also show that the Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward–Takahashi identity for general Green functions is incorporated in the model. A previous observation that the contribution of the unparticle (with scaling dimension d) to the gauge boson self-energy is a factor (2−d) of the particle’s self-energy has been extended to the Green function of triple gauge bosons. This (2−d) rule may be generally true for Green functions for any number of points of the gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.